Computerized adaptive testing has been shown to achieve better measurement precision and test efficiency by adaptively selecting and administering items to estimate a person’s unknown latent trait. Although a variety of item selection procedures have been proposed and are in use, most of them, including some Bayesian procedures, are myopic or greedy, i.e., they select the next best item given the current responses. The statistical literature demonstrates that greedy/myopic algorithms are less than optimal under most circumstances and will be optimal in only special cases. Furthermore, many current methods do not formally consider respondent burden, which can be an important consideration when computerized adaptive tests are used to measure patient-reported outcomes. A fully Bayesian adaptive sequential design optimizes over all possibilities and mathematically accounts for the possibility of asking subsequent items beyond the next one. A Bayesian adaptive sequential design also can easily incorporate both the accuracy of the estimate and the respondent burden. However, such a method is more computationally intense and challenging to implement than a greedy algorithm. In the current study we develop a fully adaptive Bayesian sequential item selection method and compare the method with the widely-used maximum Fisher’s information method and the minimum expected posterior variance method. We focus on the number of items selected, precision, and bias. For the item banks we consider, this comparison demonstrates that the fully Bayesian adaptive selection method creates shorter tests with only a slight reduction in other performance measures.
Swartz, Richard J ; Choi, Seung; and Herrick, Richard C., "Bayesian Adaptive Sequential Item Selection (BASIS): An Opmtimal Approach to Item Selection" (September 2009). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 53.